What is the answer to log_{4}(x+12)-log_{4}(5-x)=2 ?

The answer to log_{4}(x+12)-log_{4}(5-x)=2 is x=4

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log_{4}(x+12)-log_{4}(5-x)=2

lo g_{4} (x + 12) - lo g_{4} (5 - x) = 2

x = 4

Solution steps

lo g_{4} (x + 12) - lo g_{4} (5 - x) = 2

Add

lo g_{4} (5 - x)

to both sides

lo g_{4} (x + 12) - lo g_{4} (5 - x) + lo g_{4} (5 - x) = 2 + lo g_{4} (5 - x)

Simplify

lo g_{4} (x + 12) = 2 + lo g_{4} (5 - x)

Apply log rules

x + 12 = 16 (5 - x)

Solve

x + 12 = 16 (5 - x) : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

lo g_{2} (x + 7) = 5

lo g_{b} (3) = \frac{1}{2}

ln ((2 x + 3)^{3}) = 1

\frac{lo g _{10} ( 2 x ^{2} + 1 )}{lo g _{10} ( x + 1 )} = 2

40 = 20 \cdot lo g_{10} (\frac{x}{0.0002})

What is the answer to log_{4}(x+12)-log_{4}(5-x)=2 ?
The answer to log_{4}(x+12)-log_{4}(5-x)=2 is x=4
Solve for x: log_{4}(x+12)-log_{4}(5-x)=2
The solution is x=4